Using R
Say for example you have a matrix such as the one below.
> C<-matrix(c(0,-7,2,8,0,0,3,7,0,3,0,3,0,0,0,0),nrow=4,byrow=TRUE)
> C
If there is only a single minimum for each row you can find it with
apply(C, 1, which.min)
or (from R: finding column with minimum value in each row when there is a tied). See ?max.col
for more options.
max.col(-C, "first")
edit (thanks to @flodel in the comments)
You can do this for individual rows by
which.min(C[1,])
Or if there are multiple matches
apply(C, 1, function(i) which(i == min(i)))
You get 5
, as -7
is the fifth element of the matrix as it goes column wise. Look at c(C)